The table below shows the value, V, of an investment (in dollars) after n years.0312144800V(n)1914098.53 19679.6Use your calculator to determine the exponential regression equation that models the set of data above.Round the "a" value to two decimals, and round the "b" value to three decimals. Use the indicatedvariables and proper function notation.75925.69 8226.36V(n) =-Based on the your regression model, what is the percent increase per year?196Find V(15). Round your answer to two decimal places.V(15) =12449.83Interpret your answer by completing the following sentence. Be sure to use units in your answer.In"The value of the investment afterHow long will it take for the value of this investment to reach $10,000? Round your answer to twodecimal places.V(n) = 10000 when n =isInterpret your answer by completing the following sentence. Be sure to use units in your answer.Inthe value of the investment will reachHow long will it take for the value of the investment to double? Round your answer to two decimalplaces.V(n) has doubled when n =Interpret your answer by completing the following sentence. Be sure to use units in your answer.the value of the investment will double.

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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.3: Modeling Data With Power Functions

Problem 3TU

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Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?
Use the table of values you made in part 4 of the example to find the limiting value of the average rate of change in velocity.
The pressure in pounds per square inch was measured at various altitudes of h, in kilometers (km), above Earth's surface. The results are shown in the following table. Altitude (km) 0 10 20 30 40 50 60 70 80 Pressure (lb/in2) 14.7 11.91 9.315 7.64 6.129 4.637 3.676 3.193 2.358 Use exponential regression to find an exponential function for the pressure, P, at an altitude of h km. Round constants to the nearest thousandth. P = Use the model to predict the atmospheric pressure (in lb/in2) at an altitude of 19 km. Round to the nearest tenth. ? lb/in2
The increase in carbon dioxide (CO2) in the atmosphere is a major cause of global warming. Using data obtained by Charles David Keeling, professor at Scripps Institution of Oceanography, the average amount of CO2 in the atmosphere from 1958 through 2010 is approximated by A(t) = 0.012313t2 + 0.7545t + 313.9 (1 ≤ t ≤ 53) where A(t) is measured in parts per million volume (ppmv) and t in years, with t = 1 corresponding to 1958.† Find the average amount of CO2 in the atmosphere from 1958 through 2010. (Round your answer to two decimal places.) ppmv
A study of king penguins looked for a relationship between how deep the penguins dive in meters xx to seek food and how long they stay underwater in minutes yy. Based on sample data, the regression line is found to be y^=2.69+0.0116x Use the regression line to estimate how long a typical dive of 200 meters would last. Round your answer to two decimal points.
Use the regression equation to predict the energy expenditure for a house with 1250 square feet. Round to 2 decimal places. If I did this correctly to start with, it's y=0.388 (1250) +1027.554
Suppose that the value of a yacht in dollars after t years of use is V(t)=300000e^(−0.12t). What is the average value of the yacht over its first 18 years of use? V ave =____________ $
The volume V, in liters, of air in the lungs during a three-second respiratory cycle is approximated by the model V = 0.1729t + 0.1522t2 − 0.0374t3, where t is the time in seconds. Approximate the average volume of air in the lungs during one cycle. (Round your answer to four decimal places.)
The increase in carbon dioxide (CO2) in the atmosphere is a major cause of global warming. Using data obtained by Charles David Keeling, professor at Scripps Institution of Oceanography, the average amount of CO2 in the atmosphere from 1958 through 2016 is approximated by A(t) = 0.012414t2 + 0.7485t + 313.9 (1 ≤ t ≤ 59) where A(t) is measured in parts per million volume (ppmv) and t in years, with t = 1 corresponding to 1958.† Find the average rate of increase of the average amount of CO2 in the atmosphere from 1958 through 2016. (Round your answer to two decimal places.)
The owner of a movie theater company would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow. Use α = 0.01 to test the hypotheses H0: β1 = β2 = 0 Ha: β1 and/or β2 is not equal to zero for the model y = β0 + β1x1 + β2x2 + ε, where x1 = television advertising ($1,000s) x2 = newspaper advertising ($1,000s). Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places. State your conclusion. (b) Use α = 0.05 to test the significance of β1. State the null and alternative hypotheses. Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) (c) Use α = 0.05 to test the significance of β2. State the null and alternative hypotheses. Find the value of the test statistic. (Round your answer to two decimal…
The volume V, in liters, of air in the lungs during a one-second respiratory cycle is approximated by the model V = 0.1729t + 0.1522t2 − 0.0374t3, where t is the time in seconds. Approximate the average volume of air in the lungs during one cycle. (Round your answer to four decimal places.
During the first 45 seconds of a rocket flight, the rocket ispropelled straight up so that in t seconds it reaches a height (in feet) of: h(t)= (t^3)/(√10) What is the average velocity of the rocket during the first 135 feetof its flight

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